Nonlinear Damage Identification in Fiber-reinforced Cracked Composite Beams through Time-space Wavelet Analysis

It is well-known that wavelet analysis is, in the space domain, an efficient way to determinate the damage location (Pakrashi et al., 2007; Loutridis et al., 2004), while, in the time domain, it is an efficient tool to identify the system stiffness variation (Hou et al., 2000; Basu et al., 2008). Based on the idea of combining the information of the structural response in both space and time domains, a new time-space wavelet-based technique aimed at identifying the nonlinear behaviour of damage for SHM is presented. A FE model of a fiber-reinforced cantilever beam with a bridged crack is used to simulate the nonlinear static structural response. On the basis of particular conditions related to the Continuous Wavelet Transform (CWT) of the beam deflection and of the features of the 4th order Coiflets wavelet, a linear relation between the values of the relative rotation due to the crack and the normalized wavelet coefficients at the crack position is ruled out. By analysing through CWT the time sequence of the beam response in the space domain through the aforementioned linear relation, the nonlinear structural behaviour due to damage is identified. The effectiveness of the method in calibrating a small crack, is discussed with respect to the wavelet scale and the noise level.